Vacuum-insulated glass (VIG) windows (10) that employ glass-bump spacers (50) and two or more glass panes (20) are disclosed. The glass-bump spacers are formed in the surface (24) of one of the glass panes (20) and consist of the glass material from the body portion (23) of the glass pane. Thus, the glass-bump spacers are integrally formed in the glass pane, as opposed to being discrete spacer elements that need to be added and fixed to the glass pane. Methods of forming VIG windows are also disclosed. The methods include forming the glass-bump spacers by irradiating a glass pane with a focused beam (112F) from a laser (110). Heating effects in the glass cause the glass to locally expand, thereby forming a glass-bump spacer. The process is repeated at different locations in the glass pane to form an array of glass-bump spacers. A second glass pane is brought into contact with the glass-bump spacers, and the edges (28F, 28B) sealed. The resulting sealed interior region (40) is then evacuated to a vacuum pressure of less than one atmosphere.